This patent application claims priority of German Patent Application No. 100 33 575.6, filed on Jul. 11, 2000. The entire contents of the German Patent Application are hereby incorporated by reference.
1. Field of the Invention
This invention relates to a method and a device for estimating the frequency of a digital signal.
2. Related Art
A method for frequency estimation is disclosed by J. K. Wolf and J. W. Schwartz in xe2x80x9cComparison of Estimators for Frequency Offset,xe2x80x9d IEEE Transactions on Communications, vol. 38, no. 1, January 1990, pages 124-127. In this article, it is proposed that the phase of the complex digital input signal be differentiated and the differentiated phase be sent to an averaging filter. It is demonstrated in this article that the ideal pulse response of the averaging filter is parabolic. The parabolic curve of the pulse response of the averaging filter can be approximated relatively well by a trapezoidal curve with an increasing range, a constant range and a descending range. The standard deviation of the estimation error increases by only about 6% in comparison with the use of an ideal averaging filter with a parabolic pulse response. Therefore, this can be called a suboptimal frequency estimator.
If the filter with a trapezoidal pulse response mentioned in the article cited above were to be implemented directly, a relatively large number of multiplications would have to be performed because each sample within the observation interval would have to be multiplied by a corresponding coefficient.
Therefore, the object of the present invention is to provide a method and a device for estimating the frequency of a digital input signal, where the trapezoidal pulse response of the averaging filter is generated easily, preferably without a gate-intensive multiplier.
This object is achieved with regard to the method by the features of claim 1 and with regard to the device by the features of claim 6. Advantageous refinements of this invention are characterized in the subordinate claims.
The present invention makes use of the finding that the trapezoidal pulse response can be generated by superimposing two time-offset triangular pulse responses. Triangular pulse responses can be generated by folding two square-wave pulse responses, where the second triangular pulse response which is offset in time with respect to the first triangular pulse response can be generated by folding with a Dirac pulse. Square-wave pulse responses can be generated by a combination of an integrator and a differentiator, where the differentiator has a reduced sampling rate whose sampling period corresponds to the period of the square-wave pulse response, i.e., one third of the observation period. Therefore, the differentiator subtracts the initial value of the integrator from the end value of the integrator. The amplitude of the square-wave pulse response corresponds to one third of the resulting trapezoidal pulse response.
Further scope of applicability of the present invention will become apparent from the detailed description given hereinafter. However, it should be understood that the detailed description and specific examples, while indicating preferred embodiments of the invention, are given by way of illustration only, since various changes and modifications within the spirit and scope of the invention will become apparent to those skilled in the art from this detailed description.